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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-23/4, b>=a > For fixed z and a=-23/4, b=13/4





http://functions.wolfram.com/07.23.03.9855.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 13/4, 7/2, z] == (1/(333107775 Pi^(3/2) z^(5/2))) (8 (2 (403788 + 1716099 z + 21367115 z^2 - 218557647 z^3 + 662378805 z^4 - 986195584 z^5 + 797227008 z^6 - 337182720 z^7 + 58720256 z^8) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (403788 + 1716099 z + 21367115 z^2 - 218557647 z^3 + 662378805 z^4 - 986195584 z^5 + 797227008 z^6 - 337182720 z^7 + 58720256 z^8) EllipticE[(1/2) (1 + Sqrt[z])] - (403788 + 201894 Sqrt[z] + 1716099 z + 874874 z^(3/2) + 21367115 z^2 - 30874998 z^(5/2) - 218557647 z^3 + 119177190 z^(7/2) + 662378805 z^4 - 201850000 z^(9/2) - 986195584 z^5 + 177835008 z^(11/2) + 797227008 z^6 - 80166912 z^(13/2) - 337182720 z^7 + 14680064 z^(15/2) + 58720256 z^8) EllipticK[(1/2) (1 - Sqrt[z])] + (403788 - 201894 Sqrt[z] + 1716099 z - 874874 z^(3/2) + 21367115 z^2 + 30874998 z^(5/2) - 218557647 z^3 - 119177190 z^(7/2) + 662378805 z^4 + 201850000 z^(9/2) - 986195584 z^5 - 177835008 z^(11/2) + 797227008 z^6 + 80166912 z^(13/2) - 337182720 z^7 - 14680064 z^(15/2) + 58720256 z^8) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 80166912 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 797227008 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 177835008 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 986195584 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 201850000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 662378805 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02